Method for realizing secure point multiplication in chips

Abstract

The invention discloses a method for implementing a secure point product in a chip. Step 1. Read the scalar k and elliptic curve point P used for the point product operation; Step 2. Generate a random bit sequence RandomBit with a duty ratio of 1 / N ; Step 3. Compute the non-adjacent representation of the scalar k For i ∈ {1, 3, 5, ..., 2 w-1 -1}, calculate P i = iP; Step 4.Q←∞; Step 5. For i from 1-1 to 0, repeat execution; Step 5.1.Q←2Q; Step 5.2. If the lowest bit of RandomBit is 1, then execute the pseudo-operation DP, RandomBit ≥1; otherwise, if k i ≠0, and k i >0, then otherwise, Step 6. Return (Q). The invention can effectively resist side channel attack, fault injection attack and template analysis attack, and improves the security of the chip. It is suitable for embedded devices with limited computing resources such as smart cards, such as financial cards and transportation cards with cryptographic security chips.

Description

technical field [0001] The invention relates to the field of safe execution of an elliptic curve public key cryptosystem in a chip, in particular to a method for implementing a secure point product in a chip. Background technique [0002] Since Miller and Koblitz independently proposed elliptic curve public key cryptography in 1985, elliptic curve public key cryptography (elliptic curve cryptosystem, referred to as ECC) has its unique advantages, such as fast calculation speed, small storage space, low bandwidth requirements, computing The few parameters and so on have aroused great concern of cryptographers. So far, ECC has not only been widely used in the field of information security, but also formed international standards (IEEEPI1363, ANSIX9, ISO / IEC and NIST, etc.) recognized by some international organizations as public key encryption standards. The core operation of the elliptic curve public key cryptosystem is the point multiplication operation, and the efficiency ...

AI Technical Summary

Problems solved by technology

Therefore, cryptographers have proposed many security implementation methods, such as adding pseudo-operations to balance point doubling and point addition, and some transform scalars so that point multiplication operations can resist simple power analysis, etc. However, due to the endless emergence of attack methods, the current implementation method resists one attack method but cannot be immune to another attack method

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